In trying to match a target (standard) shade based on an unknown set of dyes, the first trial dyeing is frequently not acceptable. The main reasons are usually that the current dye batches are of a different shade and strength than the dye batches used to dye the primary (calibration) dyeings, the dyeability of the cloth or other substrate is different from that used for the primaries or target, the additive function used in calculation of the formulation is inaccurate, and other errors whatever they might be.
One, therefore, uses the trial dyeing to calculate a corrected formulation. Commercial algorithms used in the color formulation and correction computations are often trade secrets, so that the way that the color formulation for the trial dyeing is calculated, and the way the trial dyeing is used to correct the initial formulation are closely guarded. Often a second trial dyeing is required using the knowledge obtained from the first trial formulation and dyeing, and the process repeats until an acceptable color match is, perhaps, obtained.
Color matching is based on the a priori primary dyeings of the individual dyes. For each dye, the primary dyeings consist of a set of dyeings on cloth at a series of usually four or more concentrations. The concentrations span the usable range of the dye. Percent reflectance values versus wavelength data, the spectrum, for each concentration as well as the concentration are then stored in a dye data bank.
A spectrum, accordingly, is a plot of percent reflectance versus wavelength. The wavelength range usually covered is from four-hundred (400) to seven-hundred (700) nanometers, the visible range. Additional ranges, such as seven-hundred (700) to nine-hundred (900) nanometers (the near-infrared) can be included/covered without any basic change in the algorithms used in the computations. The percent reflectance values of a sample at given wavelengths are obtained using a spectrophotometer. These instruments are commercially available.
In a spectrophotometric match one tries to find the set of dyes which when dyed to form a trial dyeing provides a spectrum which is practically congruent with the spectrum of the target shade. Similarly, in a colorimetric match, one tries to find the set of dyes which when dyed to form the first trial dyeing provides the tristimulus values X, Y, and Z (the color coordinates in color space) which are closest to the tristimulus values of the target. Technical Report Natick/TR-90/006 titled "Color Matching Spanning the Visible and Near-Infrared: Use of the Cubic Spline Function in Interpolation", by R. A. Prosser and G. Arruda, U.S. Army Natick RD&E Center, Natick, Mass. 01760-5019, November 1989, describes a spectrophotometric algorithm for use in color formulation, incorporated herein by reference, a book entitled "The Practice of Absorption Spectroscopy", by Stearns, Wiley-Interscience at pp. 257-8 (NY, 1969), incorporated herein by reference, and reports entitled "Basic Equations Used in Computer Color Matching" by Allen, 56 J. Opt. Soc. Am 1256-9 (1966) and " Basic Equations Used in Color Matching, II. Tristimulus Match, Two-Constant Theory" by Allen, 64 J. Opt. Soc. Am. 991-3 (1974), both incorporated herein by reference, describe the colorimetric algorithms for use in color formulation.
The other references are discussed in the specification of the above-identified invention.
In the former report, a color-matching process is described where the additive function used is the Kubelka-Munk equation. It has the property that, at any given wavelength, the sum of its values for the individual a priori primary dyes used to prepare the trial dyeing adds approximately to the value for the trial dyeing. There are two steps in the color-matching process. The first step is the color formulation step. The formulation when dyed results in the first trial dyeing. The shade of the first trial dyeing rarely matches the target color well enough to be acceptable. The next step is the color correction step.
The color correction step in the former report involved an empirical correction that generated a mathematical "standard", in addition to the reflectance data for the a priori dyes and the reflectance data for the trial dyes. However, the empirical correction described therein was based on estimation, and was, therefore, primarily subjective, since it left the measure of the correction to the free judgment of the color formulator. This procedure is probably typical of those used commercially. On this basis, even experienced personnel require many more trial dyeings in trying to obtain an acceptable match.